Boundary Behavior of Holomorphic Mappings

  • Steven R. Bell

Abstract

Suppose that f: D1 → D2 is a proper holomorphic mapping between smooth bounded domains D1 and D2 contained in ℂn. There are two fundamental problems in the theory of functions of several complex variables concerning the boundary behavior of f.

Keywords

Manifold 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. (1).
    S. Bell and E. Ligocka, A simplification and extension of Fefferman’s theorem on biholomorphic mappings, Invent. Math. 57 (1980), 283–289.MathSciNetMATHCrossRefGoogle Scholar
  2. (2).
    S. Bell and H. Boas, Regularity of the Bergman projection in weakly pseudoconvex domains, Math. Ann. 257 (1981), 23–30.MathSciNetMATHCrossRefGoogle Scholar
  3. (3).
    S. Bell, Biholomorphic mappings and the \( \bar \partial \)-problem, Ann. of Math. 114 (1981), 103–113.MathSciNetMATHCrossRefGoogle Scholar
  4. (4).
    —, Analytic hypoellipticity of the \( \bar \partial \)-Neumann problem and extendability of holomorphic mappings, Acta Math. 147 (1981), 109–116.MathSciNetMATHCrossRefGoogle Scholar
  5. (5).
    M. Derridj and D. Tartakoff, On the global real analyticity of solutions to the \( \bar \partial \)-Neumann problem, Comm. Partial Diff. Eqns. 1 (1976), 401–435.MathSciNetMATHCrossRefGoogle Scholar
  6. (6).
    K. Diederich and J. E. Fornaess, Pseudoconvex domains with real analytic boundary, Ann. of Math. 107 (1978), 371–384.MathSciNetMATHCrossRefGoogle Scholar
  7. (7).
    K. Diederich and J. E. Fornaess, A remark on a paper of S. R. Belly, Manuscripta Math. 34 (1981), 31–44.MathSciNetMATHCrossRefGoogle Scholar
  8. (8).
    C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1–65.MathSciNetMATHCrossRefGoogle Scholar
  9. (9).
    J. J. Kohn, Harmonic integrals on strongly pseudoconvex manifolds, I and II, Ann. of Math. 78 (1963), 112–148 and 79 (1964), 450–472.MathSciNetCrossRefGoogle Scholar
  10. (10).
    —, Subellipticity of the \( \bar \partial \)-Neumann problem on pseudoconvex domains: sufficient conditions, Acta Math. 142 (1979), 79–122.MathSciNetMATHCrossRefGoogle Scholar
  11. (11).
    G. Komatsu, Global analytic hypoellipticity of the \( \bar \partial \)-Neumann problem, Tôhoku Math. J. Ser. 2, 28 (1976), 145–156.MathSciNetCrossRefGoogle Scholar
  12. (12).
    D. Tartakoff, The local real analyticity of solutions tob and the \( \bar \partial \)-Neumann problem, Acta Math. 145 (1980), 177–204.MathSciNetMATHCrossRefGoogle Scholar
  13. (13).
    F. Trèves, Analytic hypo-ellipticity of a class of pseudodifferential operators with double characteristics and applications to the \( \bar \partial \)-Neumann problem, Comm. Partial Diff. Eqns. 3 (1978), 475–642.MATHCrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston, Inc. 1984

Authors and Affiliations

  • Steven R. Bell
    • 1
  1. 1.Mathematics DepartmentPrinceton UniversityPrincetonUSA

Personalised recommendations